Quantum Theory

Abstract

In quantum mechanics, any physical system is completely described by a state vector $\mathinner {|{\Psi }\rangle }$ in a Hilbert space $\mathcal{H}$. A system with a two-dimensional Hilbert space is also called a qubit (quantum bit). If not otherwise stated, we consider a Hilbert space with an arbitrary but finite dimension. For two parties, Alice ($A$) and Bob ($B$), with Hilbert spaces $\mathcal{H}_{A}$ and $\mathcal{H}_{B}$ the total Hilbert space is a tensor product of the subsystem spaces: $\mathcal{H}_{AB}=\mathcal{H}_{A}\otimes \mathcal{H}_{B}$.